The Small Scale Effect on Linear Vibration of Beam-Like Nanostructures

2012 ◽  
Vol 446-449 ◽  
pp. 3432-3435
Author(s):  
Cheng Li ◽  
Lin Quan Yao
Keyword(s):  
Axial Load ◽  
Vibration Mode ◽  
Multiple Scales ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Small Scale ◽  
Transverse Displacement ◽  
Linear Vibration ◽  
Small Scale Effect ◽  
Multiple Scales Analysis

Transverse free dynamics of a beam-like nanostructure with axial load is investigated. The effects of a small size at nano-scale unavailable in classical mechanics are presented. Explicit solutions for natural frequency, vibration mode and transverse displacement are obtained by separation of variables and multiple scales analysis. Results by two methods are in close agreement.

A Nonlinear Approach for Dynamic Responses of a Nano-Beam Based on a Strain Gradient Nonlocal Theory

2014 ◽  
Vol 609-610 ◽  
pp. 1483-1488
Author(s):  
Cheng Li ◽  
Shuang Li
Keyword(s):  
Strain Gradient ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Continuum Theory ◽  
Nonlocal Theory ◽  
Dynamic Responses ◽  
Transverse Motion ◽  
Small Scale ◽  
Transverse Displacement ◽  
Nonlocal Continuum Theory

The transverse nonlinear vibration of a nanobeam fully clamped at both two ends was investigated using a strain gradient type of nonlocal continuum theory. The small scale effect was considered to the mechanical model at nanoscale. The axial elongation of the nanobeam was taken into account and the nonlinear partial differential equation governing the transverse motion was derived. Subsequently, a perturbation method was applied to the nonlinear governing equation. The dynamical responses of the nanobeam such as transverse displacement and resonant angular frequency were obtained and they were compared with those by a numerical method. The comparison indicated the validity of the present nonlinear model and the multiple-scales analysis method.

Vibration Analysis of Axially Compressed Nanobeams and its Critical Pressure Using a New Nonlocal Stress Theory

2011 ◽  
Vol 105-107 ◽  
pp. 1788-1792 ◽  
Author(s):  
Cheng Li ◽  
C.W. Lim ◽  
Zhong Kui Zhu
Keyword(s):  
Differential Equation ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Bending Moment ◽  
Nonlocal Elasticity Theory ◽  
Equation Of Motion ◽  
Basic Element ◽  
Mode Shapes

The transverse vibration of a nanobeam subject to initial axial compressive forces based on nonlocal elasticity theory is investigated. The effects of a small nanoscale parameter at molecular level unavailable in classical mechanics theory are presented and analyzed. Explicit solutions for natural frequency, vibration mode shapes are derived through two different methods: separation of variables and multiple scales. The respective numerical solutions are in close agreement. Validity of the models and approaches presented in the work are verified. Unlike the previous studies for a nonlocal nanostructure, this paper adopts the effective nonlocal bending moment instead of the pure traditional nonlocal bending moment. The analysis yields an infinite-order differential equation of motion which governs the vibrational behaviors. For practical analysis and as examples, an eight-order governing differential equation of motion is solved and the results are discussed. The paper presents a complete nonlocal nanobeam model and the results may be helpful for the application and design of various nano-electro-mechanical devices, e.g. nano-drivers, nano-oscillators, nano-sensors, etc., where a nanobeam acts as a basic element.

Small-scale effect on the mechanical properties of metallic nanotubes

2012 ◽  
Vol 101 (9) ◽  
pp. 093109 ◽  
Author(s):  
Jin Zhang ◽  
Chengyuan Wang ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Mechanical Properties ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect

Geomechanical and Fracture Network Interpretation of a Devonian Outcrop

2021 ◽  
pp. 1-16
Author(s):  
Scott McKean ◽  
Simon Poirier ◽  
Henry Galvis-Portilla ◽  
Marco Venieri ◽  
Jeffrey A. Priest ◽  
...  
Keyword(s):  
Large Scale ◽  
Multiple Scales ◽  
Fracture Network ◽  
Natural Fracture ◽  
Small Scale ◽  
Nugget Effect ◽  
Schmidt Hammer ◽  
Unconventional Reservoir ◽  
Fracture Anisotropy ◽  
Fracture Intensity

Summary The Duvernay Formation is an unconventional reservoir characterized by induced seismicity and fluid migration, with natural fractures likely contributing to both cases. An alpine outcrop of the Perdrix and Flume formations, correlative with the subsurface Duvernay and Waterways formations, was investigated to characterize natural fracture networks. A semiautomated image-segmentation and fracture analysis was applied to orthomosaics generated from a photogrammetric survey to assess small- and large-scale fracture intensity and rock mass heterogeneity. The study also included manual scanlines, fracture windows, and Schmidt hammer measurements. The Perdrix section transitions from brittle fractures to en echelon fractures and shear-damage zones. Multiple scales of fractures were observed, including unconfined, bedbound fractures, and fold-relatedbed-parallel partings (BPPs). Variograms indicate a significant nugget effect along with fracture anisotropy. Schmidt hammer results lack correlation with fracture intensity. The Flume pavements exhibit a regionally extensive perpendicular joint set, tectonically driven fracturing, and multiple fault-damage zones with subvertical fractures dominating. Similar to the Perdrix, variograms show a significant nugget effect, highlighting fracture anisotropy. The results from this study suggest that small-scale fractures are inherently stochastic and that fractures observed at core scale should not be extrapolated to represent large-scale fracture systems; instead, the effects of small-scale fractures are best represented using an effective continuum approach. In contrast, large-scale fractures are more predictable according to structural setting and should be characterized robustly using geological principles. This study is especially applicable for operators and regulators in the Duvernay and similar formations where unconventional reservoir units abut carbonate formations.

scholarly journals RFaNet: Receptive Field-Aware Network with Finger Attention for Fingerspelling Recognition Using a Depth Sensor

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2815
Author(s):  
Shih-Hung Yang ◽  
Yao-Mao Cheng ◽  
Jyun-We Huang ◽  
Yon-Ping Chen
Keyword(s):  
Receptive Field ◽  
American Sign Language ◽  
Multiple Scales ◽  
Receptive Fields ◽  
Depth Image ◽  
Small Scale ◽  
Feature Maps ◽  
Depth Sensor ◽  
Depth Images ◽  
Effective Transfer

Automatic fingerspelling recognition tackles the communication barrier between deaf and hearing individuals. However, the accuracy of fingerspelling recognition is reduced by high intra-class variability and low inter-class variability. In the existing methods, regular convolutional kernels, which have limited receptive fields (RFs) and often cannot detect subtle discriminative details, are applied to learn features. In this study, we propose a receptive field-aware network with finger attention (RFaNet) that highlights the finger regions and builds inter-finger relations. To highlight the discriminative details of these fingers, RFaNet reweights the low-level features of the hand depth image with those of the non-forearm image and improves finger localization, even when the wrist is occluded. RFaNet captures neighboring and inter-region dependencies between fingers in high-level features. An atrous convolution procedure enlarges the RFs at multiple scales and a non-local operation computes the interactions between multi-scale feature maps, thereby facilitating the building of inter-finger relations. Thus, the representation of a sign is invariant to viewpoint changes, which are primarily responsible for intra-class variability. On an American Sign Language fingerspelling dataset, RFaNet achieved 1.77% higher classification accuracy than state-of-the-art methods. RFaNet achieved effective transfer learning when the number of labeled depth images was insufficient. The fingerspelling representation of a depth image can be effectively transferred from large- to small-scale datasets via highlighting the finger regions and building inter-finger relations, thereby reducing the requirement for expensive fingerspelling annotations.

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